Question: The equation of a circle $C$ is $(x-5)^{2}+(y+7)^{2} = 16$. What are its center $(h, k)$ and its radius $r$ ?
Solution: The equation of a circle with center $(h, k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$ We can rewrite the given equation as $(x - 5)^2 + (y - (-7))^2 = 4^2$ Thus, $(h, k) = (5, -7)$ and $r = 4$.